Mercedes driver Nico Rosberg, who effectively needs to beat Hamilton this weekend to keep his slim title chances alive, was ninth quickest.

Rosberg had a spin on his first lap and damaged a front wing but managed to get out again and set a time without problems.

Media playback is not supported on this device

Further rain expected for race day at the Grand Prix in Texas

Hamilton needs to beat Rosberg by two points and Vettel by nine to seal his third title this weekend.

The big potential losers in the session were the McLaren drivers Fernando Alonso and Jenson Button, for whom these conditions give them a chance to do better than normal because the lack of power of their Honda engine is less of a penalty.

McLaren decided to make changes to their cars after the drivers' initial few laps and the decision backfired because by the time they returned to the track the conditions had worsened dramatically.

Alonso had been fifth fastest but other drivers improved as he sat in the pits having a change to his suspension settings and he dropped to 14th.

Title permutations: Can Hamilton win in Austin?

If Hamilton wins, Vettel must finish second to prevent Hamilton winning the title at the US GP

If Hamilton finishes second, Vettel must finish fifth or Nico Rosberg must win the race to prevent Hamilton winning the title

If Hamilton finishes third, Vettel must finish sixth or Rosberg must finish second

If Hamilton finishes fourth, Vettel must finish eighth or Rosberg must finish third

If Hamilton finishes fifth, Vettel must finish ninth or Rosberg must finish fourth

If Hamilton finishes sixth, the title battle will continue to the next race in Mexico, even if Vettel does not finish or collects no points. Rosberg would need to come fifth to still be in contention.

Button dropped from ninth to 16th as he returned to the pits for a change of front wing settings.

It was an eventful session, with a number of drivers having spins and lurid off-track moments.

But it was held without any spectators because the Circuit of the Americas told fans to stay away until noon local time (18:00 BST) for safety reasons. Shortly before the end of the session at 11:00 local time the track said fans could start to come in.

Qualifying is scheduled to start at 13:00 local (19:00 BST).

Mercedes F1 executive director (technical) Paddy Lowe said he expected FIA F1 director Charlie Whiting to try to run the session as planned.

Williams' development driver Susie Wolff seemed to not let the poor weather dampen her spirits

"They will take each session as it comes, just as we have done," Lowe said.

"We did ask Charlie and he has no clear idea of what the weather will definitely deliver so we will proceed as if qualifying will start at one o'clock as normal.

"It was very tricky but there is a very slim chance that P3 times could be taken as the grid. That's why we saw a lot of cars out there trying to set a time."